2. Methods to solve compound variation

The methods to solve the problems for compound variation are:

 

1. Proportion method:

 

In this method, from the given data, determine whether they are in direct or inverse proportion. Then, the value of the unknown($x$) can be determined using:

  

2. Multiplicative factor method:

 

Let us consider the table to understand how to solve the problem using the multiplicative factor method.

 

 

Here, the unknown quantity is $x$.

 

Step 1: Compare the unknown value (Quantity $1$) with the known values (Quantity $2$ and Quantity $3$).

 

Step 2: If Quantity $1$ and Quantity $2$ are in direct variation, then take the multiplying factor as $\frac{d}{b}$(take the reciprocal).

 

Step 3: If Quantity $1$ and Quantity $3$ are in inverse variation, then take the multiplying factor as $\frac{c}{e}$(no change).

 

Step 4: The value of the unknown $x$ can be determined using $x = a \times \frac{d}{b} \times \frac{c}{e}$.

 

 

3. Formula method:

 

From the given data, identify Persons($P$), Days($D$), Hours($H$) and Work($W$) and use the formula:

Here, the suffix $1$ denotes the values from statement $1$, whereas the suffix $2$ denotes the values from statement $2$.